Measurement of piezoelectric crystal characteristics



March 28, 1961 D. KOSOWSKY MEASUREMENT OF PIEZOELECTRIC CRYSTAL CHARACTERISTICS Filed April 15, 1956 TUBE -vorm VACUUM TUN AMPLI VAR! FREQ OSCILLATOR ,cost of each filter became excessive.

accompanying drawings.

'MEASUREMENT OF PIEZOELECTRIC CRYSTAL CHARACTERISTICS David I. Kosowsky, West Newton, Mass., assignor to Research Corporation, New York, N.Y., a corporation of New York Filed Apr. 13, 1956, Ser. No. 578,124

1 Claim. (Cl. 29--1'5'5.5)

This invention relates to piezoelectric crystals for wave filters, and more specifically it relates to the measurement of certain characteristics of crystals which significantly affect the properties of such filters.

In addition to their use as frequency control elements for oscillators, piezoelectric crystals have also been used as circuit elements in wave filters, particularly wave filters of the bandpass type for which they are most ideally suited. Although, in general, the band-pass characteristics of a filter employing crystals, that is a crystal filter, will be superior to an equivalent filter which employs only capacitive and inductive elements, there has not been as wide a use of crystal filters as would ordinarily be expected under these circumstances. One of the main reasons for this is that hitherto the adjustment of the crystals to conform certain of their characteristics to predetermined values as calledfor in the filter design res Patent has involved such as a large amount of labor that'the V v p Also conventional measuring techniques whereby these characteristic values ofthe crystals are established have not been sufiiciently accurate in general to permit predetermined filter specifications to be met within reasonable tolerance limits.

In many cases this has led to a trial and error process -.of selection of crystals for use in a particular filter design which is especially costly where only a relatively few units of like design are to be manufactured. I

It is an object of this invention, therefore, to provide a technique for measuring characteristics of piezoelectric crystalswhich permits such characteristicvalues as are important in the realization of a particular crystal filter design to be established quicklyv and accurately.

As a concomitant to the foregoing, it is a further ob ject of the invention to obviate much of the empirical practice generally associated wth the manufacture of crystal filters to predetermined specifications.

Thenovel features of the invention, together with further objects and advantages thereof, will become more Ireadily apparent from the following detailed description of the invention wherein reference will be had to the to represent a second piezoelectric crystal;

Fig. 4 is a graph illustrating the impedance characteristic of the crystal of Fig. 3;

Fig. 5 is a schematic diagram of a crystal filter of .lattice type configuration incorporating the crystalof- Fig. 1 in each series arm and the crystal of Fig. 3 in: each shunt arm; r

Fig. 6 is a graph illustrating the attenuation characteristic of the filter of Fig. 5;

' Fig. 7 is a schematic diagram of an illustrative: for hr- 2 of measuring circuit suitable for carrying out the method of measurement according to the present invention;

Fig. 8 is a graph illustrating the voltage output characteristic of the circuit of Fig. 7 when in a first condition; and

Fig. 9 is a graph similar to that of Fig. 8 with the circuit of Fig. 7.in a somewhat dilferent condition.

With reference first to Fig. 1 those skilled in the art will recognize that the circuit therein illustrated is equivalent .to a piezoelectric crystal in idealized form in that the resistive or dissipative component of impedance associated with the crystal has been omitted. Components L and C which are generally termed the series inductance and series capacitance, respectively, of the crystal are connected in series with one another between the terminals ofthe crystal 1-1, and component C which is generally termed the shunt capacitance, is connected in parallel with the series combination of L and C The reactance Z of the circuit of Fig. 1 as a function of frequency f is plotted in Fig. 2. From Fig. 2 it will be observed that the circuit has two critical frequencies, namely a zero at frequency f,,, the resonant frequency of the crystal where the reactance Z,, is zero, and a pole at frequency I the antiresonant frequency 0 the crystal where thereactance Z is infinite. Fig. 3 is an equivalent circuit of a second piezoelectric crystal similar to that of Fig. 1, the series inductance, series capacitance, and shunt capacitance, in this case being denoted by L C and C respectively; A plot of the reactance l of this circuit, which of course also has one zero and one pole, is shown in Fig. 4, the location ofthe 'zero being denoted by the frequency f, and the location of the pole being denoted by the frequency f i Although the shunt capacitance of a crystal C (or C can be measuredaccurately enough for most filter applications, hitherto the methods employed for measuring and adjusting theseries capacitance C or the series inductance L (for a given resonant frequency, the one determines the other) have been generally inadequate. This is particularly true as regards the most general and hence the most common type of crystal filter configuration, namely a lattice filter which incorporates at least one crystal in each series arm, such as that represented by Fig. 1, and at least one crystal in each shunt arm, such as that represented'by' Fig. 3. A simplified form of this type of filter is illustrated in Fig. 5 where'the individual crystals have been designated A and B. In a variation of this circuit two divided plate crystals (four terminals each) are utilized for the series and shunt arms respectively, instead of the four separate crystals as shown. In another" variation, a hybrid equivalentcircuit is used which has the same transmission characteristics as the lattice but requires'only a single pair of crystals (as shown for example in the Bell System Technical Journal of October, 1937, pages 423-436). Whether or not either of these well known expedients is adopted, however, is immaterial, in principle at least, to the method of the present invention.

In any case, what is important, in addition to the establishment of the proper resonant frequencies for the crystals, is the adjustment of the series capacitance C or more particularly the ratio of the series capacitance in each lattice arm namely i because this ratio directly afiects the relative positions of the attenuation maximaof the filter. It is to the measurement and adjustment of this ratio that the present invention is primarily directed.

With reference now to Fig. 6, where the attenuation a of the filter circuit of Fig.5 is plotted as a function of frequency f, it will be observed that two attenuation peaks-occur, one at frequency fe and dreamer-area quency fee? The passband ofthe*filterisdefined by frequencies 1, and f and within the pass band==are found the frequencies f5 and f all of which'correspoud to the zeros and poles, respectively, of Figs. 2 and 4. InFig.-6 the separation between 5f and f has been designated by A the'separation between feo a'nd f has been designated A and the separation between i60 and f has been designated' n Since the attenuation peaks at foe; and 'feo' oocur at frequencies where the r'eactanceZ of the crystal in each "series arm' becomes equal't'of'the reactance 'Z of the crystal in each shunt arm, it follows that:

where Y equals and Yb equals' z- The same is true irrespective'of the-relative positions of the poles and zeros of crystals A andB, and therefore,

it 'shouldbe understood that theattenuation characteristic illustrated-byway of example in Fig. =6be'ars no relation whatever to th'e' attenuation characteristic to berealized In the casewhere foo equalsfeo liqiiation ibecoines:

sedans masters ma nstays, squatter stains:

i(d caf filf fiff in the result yields:

, An approxinaate formof Equation 5 'may'beobtained by ,jrt immre f eshes f (f A9).2 =1? 2A0fa An: Substituting Equation 6 in Equation 5 i yields:

If in the bracketed expressions of Equation 7 A and A, are neglected then Equation 7 becomes:

The error. involved in this approximation is negligible for all practical purposes since A and A will always be relatively insignificant as compared with 2 and 2 respectively. d

In Fig. 7 there is shown an illustrative form of circuit to carry out the method of measurement according to the present invention.- As shown in Fig. 7, with switches 11-14 in their at positions, the crystals A and B of Figs. 1 and 3 are connected in a lattice (or bridge) configuration like that of Fig. 5, one each of the series and shunt arms being represented by the dotted lines 15 and 1d, respectively, to simplify the drawing. In other words, dotted line 15 represents a crystal just like the series'arm crystal 'Aand dotted line '16 represents a crystal just like the shunt arm crystal B. In practice this result follows naturally rornthejuse of divided plate crystals or the hybrid equivalent circuit mentioned heretofore. Connected to'the one end of the lattice is an input circuit including a transformer '17 with a capacitor 13 across its "secondary windingand-'a-capacitor319 in series with its primarywinding, the latter in'turn being connected to a variable frequency oscillatorlt). Connected to the other =eiid of the-lattice isan outputcircuit which includes a -tran'sformer 21 having a pair ofcapacitors '22 and 23 connected across its; primary and secondary. windings respectively. *This;output*cir'cuit"is in turn coupled to a "tuned'amplifier 24 through a switch-25am the amplifier iskoupldtof-a vacuum tubeQvolt irieter 26. Finally, a I bf calibrated tiariable capacitors 27 "andZS" are con- "n'ected across' the crystals-A andh th'rough switches29 and-fiflrespect'iv'ely.

- d An additional circuitis provided between the oscilla- "torzo and the amplifier 24 whereby the individual crystals may be selectively connected directly between the oscillator-and the amplifier. Thus, one of the'output termi- "nals of the oscillator is connected to the y terminals of switches -11, -1;3-and-theother output terminal of the oscillator is connectedto a common point or ground. "To complete the'circuit there are provided individual ijconnections from'the'y terminals of switches '12-'and'14 fto the y terminal of switch 25; and a pair of resistors 31 and 32: '5 "Resistor 61, which is of relatively 'lowvalue (1-10 0'oh'ms depending onfrequency is connected tom 'the ungroundedterminfl of oscillator 20 to ground,' and resistor 32,- whiclr-has avalue similar tothat of resistor =31,'.-is connected from the y 'terminalof' switch 12 to ground -'In*oper'ation,-'-switeh 25 is placed-in its y position, switches 13 and 14 -arep1aced in their 2: positions, and 'switches-1Pand 12m placed in their y'positions. Under -:these conditions a-s'imple "measuring circuit is 'formed whereby the resonant frequency-"of crystal *A may be measured or adjusted as required. To measure the fre- 60 c'iuency'of' "crystal A,- the frequencyof' 'oscillatoritl is adjusted until the indication provided by the vacuum tube voltr'neter26'is a'maximum. "This corresponds to the resonant frequency f of crystal'A as indicated'in -8-. *The resonant trequency'of-theshunt crystal B 6E5 may be similarlyimeasured ifthe' relativepositionsof switches 11- =an 1 12, "on the onehand; and switches 13 e and 14 on the other be reversed. Thus', switches ll'and 12 are placed in menrspeeuv J c' positiona' switohes 13 I and'l i are placed in their respective y-p'ositidns, and 'the fos'cillator is once' again adjusted for a maximum -indication of the vacuum tube voltmeter, such maximum corresponding: ftowthe: resonant: frequencyf -'-'of crystal B. Having determined the resonant frequencies lof'both 3 s r ess-andas t cry alsrAvand- Btwhichi defines the value of A}, (Fig. 6), switches 11-14 are each placed in their x positions, switches 29 and 30 aie closed if this has not already been done, and'switch 2 5 is moved toits lattice being coupled to the oscillator 20, and the output end of the lattice being coupled to the amplifier 24 and vacuum'tube voltmeter 26. Oscillator 20 is then set to a frequency which is less than the frequency f,,, and the capacitors 27 and 28 are adjusted for a minimum indication on :the vacuum tube voltmeter, corresponding to an attenuation maximum. In this way, the frequency of maximum attenuation foo (Fig. 6) is made to coincide with the oscillator frequency and A is caused to equal the difference between the oscillator frequency and the resonant frequency f,,. Next the oscillator frequency is increased until the other attenuation maximum or peak at feo is located, the frequency difference between f and f corresponding to A in Fig. 6. The ratio may now be determined by substituting in Equation 8.

can be measured increases as A increases. On the other hand, when A is relatively large, it is difiicult to distinguish the position of the attenuation peak at f because of system noise. In general, a good compromise is obtained when A is in the order of IOA With respect to the frequency difference A itself, the choice of A will depend somewhat on the type of filter application for which the crystals are intended. If the crystals A and B are to be used in a narrow band filter then the frequencies f,,, f, which define A can be the resonant frequencies called for in the filter design. If the crystals are to be employed in a wide band filter, however, their resonant frequencies will be too widely separated, and in this case two alternatives are possible.

According to one alternative, the resonant frequency of the crystal A as called for in the filter design is chosen as the frequency ;f,, and the crystal B is adjusted to a frequency f about .1% of f,, cycles (A above f,,. The ratio is then measured and the crystals adjusted until the measured value of and (12,) are the values called for in the filter design. Accordingly, when the resonant frequency of crystal B is subsequently raised to its ultimate value (f,,) by further adjustment (grinding) of crystal B, then the series capacitance Q, will be correspondingly decreased so that the 8 final ratio of the series B will be as desired.

.The second alternative for the wide band filter case is most useful where a pair of crystals have already been adjusted for use in a particular filter design, and it is a duplication of these crystals for additional filters of like design which is desired. If the crystals to be duplicated an. amount A where A is about .1% of f cycles. As.

previously described, the circuitof Fig. 7 is collaterally adapted to measure crystal resonant frequency, and hence the resonant frequency of crystal A may be measured and adjusted by simply substituting crystal A for crystal A or B. Once the new resonant frequency of crystal A has been established, crystal A, is substituted for crystal B in .Fig. 7. Any crystal may now be made identical to crystal A as it was beforeits resonant fre-' quency was increased (the condition to be duplicated), by substituting such crystal for crystal A in Fig. 7, and adjusting it until its resonant frequency equals 1'', and the capacitance ratio equals 1, as measure according to the procedure described in connection with crystals A and B. It is apparent crystal B may serve as a standard to be duplicated by other crystals in similar fashion. The accuracy of measurement of the ratio resulting from these techniques can be shown to be roughly times greater than could be obtained hitherto,

assuming the same accuracy of oscillator frequency indications.

With reference now to Figs. 8 and 9, it will be shown that collaterally the individual values of shunt capacitances C C and series capacitance C C of the crystals A and B may also be measured with the circuit of Fig. 7 in accordance with hitherto known procedure. To measure these parameters with respect to crystal A, for example, switches 13 and 14 are placed in their x positions, switches 11 and 12 are placed in their y positions, and switch 29 is opened. It will be recalled that this is substantially the same state of affairs which o'btains when the resonant frequency of crystal A is to be measured. However, in this case it is necessary to measure the antiresonant frequency (pole) of the crystal A as well as its resonant frequency (zero), and to this end the frequency of the oscillator is adjusted until the vacuum tube voltmeter indicates a minimum corresponding to the frequency f of Fig. 8. Next the switch 29 is closed and capacitor 27 adjusted to a predetermined value which will be denoted C The effect of the capacitor 27 across the crystal is to decrease its antiresonant frequency to a new value corresponding to the frequency f of Fig. 1. If 3,, is defined as the frequency diiference between f and f and S is defined as the frequency difference between and f (as shown in Figs. 8 and 9), it can be shown that,

from which the shunt capacitance C and series capacicapacitances of crystals and tance C may be easily calculated. The shunt capacitance C of crystal B may be determined in similar fashion by reversing the positions of switches 11 and 12 with respect to switches 13 and 14.

Although the method of measurement according to the present invention has been described in, connection with an illustrative circuit which is collaterally adapted to measure, resonant frequency and shunt capacitance, it is, apparent that the circuit maybe simplified considerably if it is to be used only for measuring series capacitance ratio. Variousmodifications of this nature which remain within thetspirit andscope of the inventionwill no doubt occur to those skilled, in the art.

Therefore, what isclaimed is In a method of manutacturing a crystal filter with predetermined transmission characteristics, including at least a first piezoelectric element of known resonant frequency and a second piezoelectric element of known resonant frequencydifierentsfrom theresonant frequency of said first element andhaving its series, capacitance related to that of said. first element in apredetermined ratio, the steps of forming with each of said elements a test network having the transmission characteristics of a symmetrical lattice network, said transmission character istics differing from those of said filter, measuring the frequencies of attenuation of the network for relation with the resonant frequencies to determine the series capacitance ratio between said elements, adjusting the series capacitance of at least one of said elements to obtain said predetermined ratio, and forming with said elements said filter with said predetermined characteristics.

OTHER REFERENCES Lowrie: Lattice-Type Crystal Filter, Electronics, vol. 24, issue 4, April 1951, pp. 129-131.

Gerber: Proceedings of the I.R.E., vol. 41, No. 9, September v1953, pp. 1103-1 112. 

